for bounded functions f, g
on a probability space, where the norm is the supremum norm.
A related inequality that we refer to as "strong" is also shown
to hold. We show that these in fact hold also for noncommutative
probability spaces. We extend this to the case of matricial seminorms
on a unital C*-algebra, which leads us to treat also the case of
a conditional expectation from a unital C*-algebra onto a
unital C*-subalgebra.

Acknowledgements

The research reported here was supported in part by National Science Foundation grant DMS-1066368